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Finite Subgroups of the Plane Cremona Group
 IN ALGEBRA, ARITHMETIC AND GEOMETRY: MANIN FESTSCHRIFT (BIRKHÄUSER
, 2009
"... This paper completes the classic and modern results on classification of conjugacy classes of finite subgroups of the group of birational automorphisms of the complex projective plane. ..."
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Cited by 73 (6 self)
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This paper completes the classic and modern results on classification of conjugacy classes of finite subgroups of the group of birational automorphisms of the complex projective plane.
Problems in the Steenrod algebra
 Bull. London Math. Soc
, 1998
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development ..."
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Cited by 30 (1 self)
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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below. Contents 1 Historical background 4
The module structure of a group action on a polynomial ring: a finiteness theorem
 Invariant theory in all characteristics, 139–158, CRM Proc. Lecture Notes
, 2004
"... We consider a polynomial ring S in n variables over a finite field k of characteristic p and an action of a finite group G on S by homogeneous linear substitutions. This is equivalent to taking the symmetric powers of an ndimensional kGmodule. We want to understand S as a kGmodule in a manner as ..."
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Cited by 16 (4 self)
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We consider a polynomial ring S in n variables over a finite field k of characteristic p and an action of a finite group G on S by homogeneous linear substitutions. This is equivalent to taking the symmetric powers of an ndimensional kGmodule. We want to understand S as a kGmodule in a manner as explicit as possible. The
Classifying Spaces and Homology Decompositions, from: “Homotopy Theoretic Methods
 in Group Cohomology”, Advanced Courses in Mathematics CRM
, 2001
"... Abstract. Suppose that G is a finite group. We look at the problem of expressing the classifying space BG, up to mod p cohomology, as a homotopy colimit of classifying spaces of smaller groups. A number of interesting tools come into play, such as simplicial sets and spaces, nerves of categories, eq ..."
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Cited by 12 (0 self)
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Abstract. Suppose that G is a finite group. We look at the problem of expressing the classifying space BG, up to mod p cohomology, as a homotopy colimit of classifying spaces of smaller groups. A number of interesting tools come into play, such as simplicial sets and spaces, nerves of categories, equivariant homotopy theory, and the transfer. Contents
ON THE CLASSIFICATION OF FINITE GROUPS ACTING ON HOMOLOGY 3SPHERES
"... In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3sphere is the alternating or dodecahedral group A5. Here we characterize finite nonsolvable groups that act on a homology 3sphere preserving orientation. We find exactly the finite nons ..."
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Cited by 12 (11 self)
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In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3sphere is the alternating or dodecahedral group A5. Here we characterize finite nonsolvable groups that act on a homology 3sphere preserving orientation. We find exactly the finite nonsolvable groups that act orthogonally on the 3sphere, plus two families of groups for which we do not know at present if they really can act on a homology 3sphere. 1.
Propagating sharp group homology decompositions
 Adv. Math
, 2006
"... Abstract. A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either the subgroups in C or their centralizers or their normalizers. We give a short but systematic study of the relationship among such formulas for nine ..."
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Cited by 7 (0 self)
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Abstract. A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either the subgroups in C or their centralizers or their normalizers. We give a short but systematic study of the relationship among such formulas for nine standard collections C of psubgroups, obtaining some new formulas in the process. To do this, we exhibit some sufficient conditions on the poset C which imply comparison results.
Some results and conjectures on finite groups acting on homology spheres
, 2005
"... Abstract. This is a note based on a talk given in the Workshop on geometry and topology of 3manifolds, Novosibirsk, 2226 August 2005. We consider the class of finite groups, which admit arbitrary, i.e. not necessarily free actions on integer and mod 2 homology spheres, with an emphasis on the 3 a ..."
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Cited by 5 (5 self)
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Abstract. This is a note based on a talk given in the Workshop on geometry and topology of 3manifolds, Novosibirsk, 2226 August 2005. We consider the class of finite groups, which admit arbitrary, i.e. not necessarily free actions on integer and mod 2 homology spheres, with an emphasis on the 3 and 4dimensional cases. We recall some classical results and present some recent progress as well as new results, open problems and the emerging conjectural picture of the situation. We are interested in the class of finite groups, and in particular in finite nonsolvable and simple groups, which admit actions on integer and mod 2 homology spheres (arbitrary, i.e. not necessarily free actions), with an emphasis on the 3 and 4dimensional case. We present some classical results, some recent progress as well as new results, open problems and the emerging conjectural picture of the situation. 1. Basic problem. Which finite groups G admit orientationpreserving smooth actions on certain classes of manifolds: spheres Sn, integer homology spheres, mod 2 homology spheres (i.e., homology with coefficients in the integers Z2 mod 2). We consider only orientationpreserving, faithful, but not necessarily free actions (in general, the free case is classical, the main new results presented concern nonfree actions). Particular emphasis will be on dimension three. We note that every finite group admits a free action on a rational homology 3sphere [4]. Also, any finite group admits a faithful orthogonal action on a sphere (by choosing a linear faithful representation); on the other hand, the classes of groups admitting free actions on integer or mod 2 homology spheres are very restricted. The most important single case is that of the 3sphere. If an action of a finite group G on S3 is nonfree then, by Thurston’s orbifold geometrization theorem, it is Zimmermann, B.P., Some results and conjectures on finite groups acting on homology spheres.